簡約 (3^{2/3}*5^{1/4})^6

解

簡約

(3^{\frac{2}{3}} \cdot 5^{\frac{1}{4}})^{6}

405 \cdot 5^{\frac{1}{2}}

十進法表記

905.60753 \dots

解答ステップ

(3^{\frac{2}{3}} \cdot 5^{\frac{1}{4}})^{6}

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

(3^{\frac{2}{3}} \cdot 5^{\frac{1}{4}})^{6} = (3^{\frac{2}{3}})^{6} (5^{\frac{1}{4}})^{6}

= (3^{\frac{2}{3}})^{6} (5^{\frac{1}{4}})^{6}

(3^{\frac{2}{3}})^{6} = 81

= 81 (5^{\frac{1}{4}})^{6}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}, a \geq 0

(5^{\frac{1}{4}})^{6} = 5^{\frac{1}{4} \cdot 6}

= 81 \cdot 5^{\frac{1}{4} \cdot 6}

\frac{1}{4} \cdot 6 = \frac{3}{2}

= 81 \cdot 5^{\frac{3}{2}}

5^{\frac{3}{2}} = 5 \cdot 5^{\frac{1}{2}}

= 81 \cdot 5 \cdot 5^{\frac{1}{2}}

数を乗じる:

81 \cdot 5 = 405

= 405 \cdot 5^{\frac{1}{2}}